A Completely Randomized Design with Random Treatment Effects
A company employs many personnel officers.
- Five officers were selected at random.
- Each officer rated 4 candidates.
Ratings are from 0–100.
The company wants to know:
Treatment structure: One-way: Officer (5 levels – officer A, B, C, D, E)
Experimental structure: Officers were randomly assigned to interview r = 4 candidates (e.u.) in a CRD. The rating is recorded for each candidate (m.u.).
# A tibble: 20 × 3
officer candidate rating
<fct> <fct> <dbl>
1 A 1 76
2 A 2 65
3 A 3 85
4 A 4 74
5 B 1 59
6 B 2 75
7 B 3 81
8 B 4 67
9 C 1 49
10 C 2 63
11 C 3 61
12 C 4 46
13 D 1 74
14 D 2 71
15 D 3 85
16 D 4 89
17 E 1 66
18 E 2 84
19 E 3 80
20 E 4 79
\[y_{ij}=\mu+t_i+\epsilon_{ij} \text{ for } i=1,2,3,4,5; j=1,2,3,4\]
with:
where:
Linear mixed model fit by REML ['lmerMod']
Formula: rating ~ (1 | officer)
Data: personnel_data
REML criterion at convergence: 145.2
Scaled residuals:
Min 1Q Median 3Q Max
-1.3841 -0.8901 0.2620 0.6496 1.2605
Random effects:
Groups Name Variance Std.Dev.
officer (Intercept) 80.41 8.967
Residual 73.28 8.561
Number of obs: 20, groups: officer, 5
Fixed effects:
Estimate Std. Error t value
(Intercept) 71.450 4.444 16.08
Estimating Variances
Estimating the Overall Mean
Analyze > Fit ModelAttributes > Random EffectREML